The Swiss 33-year-old, ranked number two in the world, defeated Pouille, just 20 and ranked 176th, 6-4, 6-4 in a match at the Bercy indoor stadium that lasted one hour and 15 minutes.
"It was a difficult match against an opponent who had nothing to lose but I played well even if he put me under pressure and I'm very satisfied," said Federer of his 14th victory in a row.
"I feel pretty good and fresh in my head despite a lot of matches lately so now looking forward to tomorrow (Friday)."
Federer now moves on to face seventh-ranked Canadian Milos Raonic in the quarterfinals.
Earlier, Switzerland’s Stan Wawrinka, ranked fourth in the world, was knocked out of the tournament by 17th-ranked South African Kevin Anderson in a tightly contested three sets.
The tall (203 centimetres) Anderson prevailed 6-7 (2-7), 7-5, 7-6 (7-3), serving 18 aces on his way to a hard-fought victory in a match that lasted three hours.
Wawrinka, winner of this year’s Australian Open, has not won a tournament since he defeated Federer in the Monte Carlo Masters in April this year.
Scotland's Andy Murray, meanwhile, guaranteed his place at the upcoming World Tour Finals in London as he breezed to a 6-3, 6-3 third-round victory over Bulgarian Grigor Dimitrov.